Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
354 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×#3633 |
| commutator, socle | C2×C17 | C2×C82 |
| Fitting | C17×M32 | C8 |
| prime radical | C22×D17 | C4×C8 |
| cosocle | C8×#595 | C23 |
| hypercenter | M32 | #3633 |
| hypocenter | C17 | C8×M32 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C8 ◁ M32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14545799 | C2 | semidirect |
| 4. C16×#3633 | C2 | semidirect |
| 21. #10587670 | C8 | semidirect |
| 25. #10587666 | C8 | semidirect |
| 28. #10587538 | C8 | semidirect |
| 33. #10587530 | C8 | semidirect |
| 35. C17×M32 | C8 | semidirect |
| 36. #10587483 | C8 | semidirect |
| 37. #10587469 | C8 | semidirect |
| 51. #63241 | C2×C8 | semidirect |
| 58. #63216 | C2×C8 | semidirect |
| 59. C16×C17 | C2×C8 | semidirect |
| 60. #63214 | C2×C8 | semidirect |
| 67. #3633 | M32 | direct (N × H) |
| 121. M32 | #3633 | direct (N × H) |
| 132. C17 | C8×M32 | semidirect |
| 154. C16 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #595⋊M32 | 2 |
| C2×C8×#3633 | 2 |
| #14545799 | 2 |
| C16×#3633 | 2 |
| M32×#595 | 2 |
| C8×M32 | 17 |